$y = x+ 2$

$y=2x -3$

$y=x-2$

$y =4x$

The above all are example of linear function

$y=2x -3$

$y=x-2$

$y =4x$

The above all are example of linear function

For $f : R \rightarrow R$ , y = f(x) = mx + c for each $x \in R$

Domain = R

Range = R

For $y = f(x) = mx + c$ \(m\) is the slope and \(c\) is the \(y\) intercept of the graph.

If \(m\) is positive

then the line rises to the right and if \(m\) is negative then the line falls to the right

Below are few graph based on values of m and c

Identify Function and constant function are special cases of Linear function

if m =1 and c=0, Linear function becomes f(x) =x which is a identity function

If m=0 ,then Linear function becomes f(x) =c which is a Constant function

a. $y =2x$

b. $y = 11 -x$

c. $ y= \frac {2}{3} x + \frac {1}{4} $

d. $ x^2 + y^2=1$

e. $y =x^3$

f. $y =x^2 +1$

For the function to be a Linear function ,it should be of the form (mx+c)

a. This is Linear function as of the form (mx+c)

b. This is Linear function as of the form (mx+c)

c. This is Linear function as of the form (mx+c)

d. This is not a linear function

e. This is not a linear function

f. This is not a linear function

2. which of the graph represent Linear function?

The graph should be straight line for the function to be constant function

So C and D are constant function

3. Let f = {(1,1), (2,3), (0, -1), (-1, -3)} be a linear function from Z into Z.

Find f(x).

Since f is a linear function, f (x) = mx + c. Also, since $(1, 1), (0, - 1) \in Function$,

f (1) = m + c = 1 and f (0) = c = -1. This gives m = 2 and so,f(x) = 2x - 1.

- Cartesian Products
- |
- What is relations?
- |
- What is Function
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- Domain of Function
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- Range of Function
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- Identity Function
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- Constant Function
- |
- Linear Function
- |
- Modules Function
- |
- Greatest Integer Function
- |
- Polynomial Function
- |
- Algebra of Real Function

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Class 11 Maths Class 11 Physics